The present invention relates to digital infinite impulse response (IIR) filters. Infinite impulse response filters are filters with an impulse response that has an infinite length. Such an IIR filter can be built by feeding back the output into the filter.
An important class of infinite impulse response filters can be described by the difference equation EQU y[n]=b.sub.0 x[n]+b.sub.1 x[n-1]+ . . . +b.sub.M x[n-M]-a.sub.1 y[n-1]-a.sub.2 y[n-2]- . . . -a.sub.N4 y[n-N]
where X[n] is the input, Y[n] is the output of the filter, and [a.sub.1, a.sub.2 . . . , a.sub.N ] and [b.sub.0, b.sub.1 . . . b.sub.M ] are real value coefficients. An example of such a filter is given in FIG. 1. FIG. 1 shows a second order filter which is given by the equation EQU y[n]=b.sub.0 x[n]-a.sub.1 y[n-1]-a.sub.2 y[n-2]
This filter has three independent parameters b.sub.0, a.sub.1, a.sub.2. If a reconfigurable filter is desired to have a stable gain, the coefficients must be carefully chosen to maintain this stable gain. For example, if either coefficient a.sub.1, or a.sub.2 is changed, coefficient b.sub.0 should be modified to maintain a constant gain. It requires a lot of technical resources to store coefficients of such a reconfigurable system. Additionally, in order to maintain filter stability, the coefficients must be very accurately determined, since the filters can be sensitive to coefficient rounding errors.
Because of these limitations, it is desired to have an improved reconf igurable infinite impulse response filter.